(a) P and Q are points on the parallel of latitude 68.7°S, their longitudes being 124°W and 56°E respectively. What is their distance apart measured along the parallel of latitude? [Take R = 6400km, \(\pi = 3.142\)]. (Give your answers to 3 significant figures).
(b) A bag contains four red, three white and five green balls. (i) If one ball is picked at random, what is the probability that it is not green? (ii) if two balls are picked at random without replacement, what is the probability that one is red and the other white?
Explanation
(a) 
Difference in longitudes = 124° + 56° = 180°
Distance PQ = \(\frac{180°}{360°} \times 2\pi r\)
where \(r = R \cos \theta\)
\(/PQ/ = \frac{180}{360} \times 2 \times 3.142 \times R \cos 68.7°\)
\(/PQ/ = 3.142 \times 6400 \times 0.3633\)
= \(7305.53 km\)
\(\approxeq 7300 km\) (3 sig. figs)
(b) Red balls = 4, white = 3 ; green = 5
Total = 4 + 3 + 5 = 12 balls.
(i) P(green) = \(\frac{5}{12}\)
P(not green) = \(1 - \frac{5}{12} = \frac{7}{12}\)
(ii) P(picking red and white) = P( red then white) or P(white then red)
= \(\frac{4}{12} \times \frac{3}{11} + \frac{3}{12} \times \frac{4}{11}\)
= \(\frac{2}{11}\)